You can do either, however, if you can get your router to do the work, then if you take your Mac to another location, your fixed IP address will not get in your way. Generally I like to give my Mac's System Preferences -> Network -> Advanced -> TCP/IP -> DHCP Client ID a simple value that makes it easier for most routers to identify that this is the same Mac it saw the last time it connected to the network.
Yes, I understand your Mac mini is not likely to go wondering off and then return, but if you get a laptop, or iPhone, iPad, iPod Touch, other device on your network, and your router is re-assigning the same fixed IP addresses, it will make life easier for you when you want to connect via IP address between any of your devices. Configuring each device separately is just annoying.
Another trick is to arrange for both the WiFi and Ethernet interfaces to get the same Fixed IP address from the router. That way if the device (a laptop for example) normally uses WiFi, but you find a large file transfer is going slow, you plug it into an Ethernet port, and since it is the same IP address, it will transparently switch from WiFi to Ethernet and get much faster file transfer, without interrupting the in-progress file transfer.
However, if you prefer making the assignment to your Mac mini, there is nothing wrong with this, as long as when you get a new router, you make sure it is still using the same IP address range. Some routers like 10.0.0.*, some like 192.168.0.*, some like 192.168.1.*, some like 192.168.2.*, so if you switch routers and it uses a different IP range, you may forget that you have your Mac mini talking on a different range, and then wonder why it stopped using fast ethernet, and has switched to slower WiFi because WiFi is still using DHCP assigned IP addresses.